Getting more memory is probably not what you need. That configuration (3 1G sticks plus 1 2G) is not ideal but it's not bad either, esp. since it's working fine.
If you really want to improve gaming performance, you're gong to need to upgrade the graphics card with something a little more powerful. The Radeon HD 4350 is an entry level card and not really suitable for any serious gaming unless all you play is stuff like Angry Birds. What kinds of games do you want to be able to play?
Depneding on what you want to play, you probably wil want more from your CPU as well. The Phenom X4 9550 that you have is not really up to snuff for most newer games and even for the ones with lower requirements such as WOW or Diablo III it's pretty far towards the low end.
I would say that you probably need to be thinking about a new build and either scrap, donate or sell your current machine. Based on the link you provided,
http://www.newegg.com/Product/Prod [...] 883107710 you can't even install a Phenom II in that motherboard, so it's probably not worth it to upgrade to a high end graphics card. The most that I woud consider putting in there would be a Radeon HD 6670 or maybe a Radon HD 7750 card. However, having had experience with HP systems with older PCIe slots, you may not be able to get those cards to work because your motherboard may not support PCIe version 2.0 and above.